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Bulletin of the American Mathematical Society

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Elliptic operators and the decomposition of tensor fields


Author: Murray Cantor
Journal: Bull. Amer. Math. Soc. 5 (1981), 235-262
MSC (1980): Primary 58G99, 35J15
DOI: https://doi.org/10.1090/S0273-0979-1981-14934-X
MathSciNet review: 628659
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  • 1. R. Abraham and J. Marsden, Foundations of mechanics, Benjamin, New York, 1978. MR 515141
  • 2. S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12 (1959), 623-727. MR 125307
  • 3. J. Arms, A. Fischer and J. Marsden, Une approche symplectique pour des théorèmes de decomposition en géometrie ou relativité generale, C.R. Acad. Sci. Paris Sér. A 281 (1975), 517-520. MR 388447
  • 4. M. Berger and D. Ebin, Some decompositions of the space of symmetric tensors of a Riemannian manifold, J. Differential Geom. 3 (1969), 379-392. MR 266084
  • 5. J. P. Bourguignon, D. Ebin and J. Marsden, Sur le noyau des operateurs pseudo-differential a symbole surjectif et non injectif, C.R. Acad. Sci. Paris Sér. A 282 (1975), 867-870. MR 402829
  • 6. M. Cantor, The existence of non-trivial asymptotically flat initial date for vacuum spacetimes, Comm. Math. Phys. 57 (1977), 83-96. MR 462440
  • 7. M. Cantor, On the existence of asymptotically flat initial data sets for spacetimes containing manifolds with ends, preprint, August, 1979. MR 543911
  • 8. M. Cantor, A necessary and sufficient condition for York data to specify an asymptotically flat spacetime, J. Math. Phys. 20 (1979), 1741-1744. MR 543911
  • 9. M. Cantor, Perfect fluid flows over R, J. Funct. Anal. 18 (1975), 73-84. MR 380872
  • 10. M. Cantor, Some problems of global analysis on asymptotically simple manifolds, Compositio Math. 38 (1979), 3-35. MR 523260
  • 11. M. Cantor, Spaces of functions with asymptotic conditions, Indiana Univ. Math. J. 24 (1974), 897-902. MR 365621
  • 12. M. Cantor and D. Brill, The Laplacian on asymptotically flat manifolds and the specification of scalar curvature, Compositio Math. (to appear). MR 632432
  • 13. Y. Choquet-Bruhat and D. Christodoulou, Elliptic systems in Hilbert spaces on manifolds which are euclidean at infinity, Acta. Math. 146 (1981), 129-150. (Also see C.R. Acad. Sci. Paris Sér. A-B 290 (1980), 781-785.) MR 594629
  • 14. D. Christodoulou, The boost problem for weakly coupled quasilinear hyperbolic systems of the second order, preprint, February, 1980. MR 616009
  • 15. D. Ebin, The manifold of Riemannian metrics, Proc. Sympos. Pure Math., vol. 15, Amer. Math. Soc., Providence, R.I., 1970, pp. 11-40. MR 267604
  • 16. A. Fischer and J. Marsden, The initial value problem and the dynamical formulation of general relativity, General Relativity (S. Hawking and W. Israel, eds.), Cambridge Univ. Press, New York and London, 1979, pp. 138-211.
  • 17. A. Fischer and J. Marsden, Linearization stability of nonlinear partial differential equations, Proc. Sympos. Pure Math., vol. 27, Amer. Math. Soc., Providence, R.I., 1975, pp. 219-263. MR 383456
  • 18. D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, New York, 1977. MR 473443
    18a. H. Helmholtz, Über Integrale der Hydrodynamischen Gleichungen, welch den Wirbelbewegungen, J. Reine Angew. Math. 55 (1858), 25-55.

    18b. V. W. Hodge, Theory and applications of harmonic integrals, 2nd ed., Cambridge Univ. Press, New York and London, 1952. MR 51571

    18c. K. Kodaira, Harmonic fields in Riemannian manifolds, Ann. of Math. (2) 50 (1949), 587-665. MR 31148

    18d. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443-492. MR 181815

  • 19. S. Lang, Differentiable manifolds, Addison-Wesley, Reading, Mass., 1972.
  • 20. R. Lockhart, Fredholm properties of a class of elliptic operators on noncompact manifolds, preprint, 1979. MR 610188
  • 21. J. Marsden, Applications of global analysis in mathematical physics, Publish or Perish, Boston, Mass., 1974. MR 646816
  • 22. R. McOwen, Behavior of the Laplacian on weighted Sobolev spaces, Comm. Pure Appl. Math. 32 (1979), 783-795. MR 539158
  • 23. R. McOwen, On elliptic operators in R, Comm. Partial Differential Equations (to appear). MR 584101
    23a. C. Morry, Multiple integrals in the calculus of variations, Springer-Verlag, Berlin and New York, 1966. MR 202511

    23b. C. Morry and J. Eells, A variational method in the theory of harmonic integrals, Ann. of Math. (2) 63 (1956), 91-128. MR 87764

  • 24. L. Nirenberg and H. Walker, Nullspaces of elliptic partial differential operators in R, J. Math. Anal. Appl. 42 (1973), 271-301. MR 320821
  • 25. R. Palais, Foundations of global non-linear analysis, Benjamin, New York, 1968. MR 248880
  • 26. R. Palais, Seminar on the Atiyah-Singer Index Theorem, Ann. of Math. Studies, no. 57, Princeton Univ. Press, Princeton, N.J., 1965. MR 198494
  • 27. M. Protter and H. Weinberger, Maximum principles in differential equations, Prentice Hall, Englewood Cliffs, N.J., 1967. MR 219861
  • 28. F. Warner, Foundations of differential manifolds and Lie groups, Scott, Foresman and Co., Glenview, II., 1971. MR 295244
  • 29. J. W. York, Covariant decompositions of symmetric tensors in the Theory of gravitation, Ann. Inst. H. Poincaré Sect. A (N.S.) 21 (1974), 319-332. MR 373548
  • 30. K. Yoshida, Functional analysis, 3rd ed., Springer-Verlag, New York, 1971.

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DOI: https://doi.org/10.1090/S0273-0979-1981-14934-X

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